scholarly journals Frictionless Contact Problem between an Elastic Layer Bonded to a Rigid Support and a Rigid Stamp

2001 ◽  
Vol 6 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Volkan Kahya ◽  
Ahmet Birinci ◽  
Ragıp Erdöl
Keyword(s):  
Contact Problem ◽  
Elastic Layer ◽  
Rigid Support ◽  
Frictionless Contact ◽  
Rigid Stamp

Frictional contact problem of an anisotropic laterally graded layer loaded by a sliding rigid stamp

2020 ◽  
Vol 234 (10) ◽  
pp. 2024-2041
Author(s):  
Onur Arslan
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Computational Methods ◽  
Singular Integral ◽  
Elastic Layer ◽  
Frictional Contact ◽  
Lateral Direction ◽  
Frictional Contact Problem ◽  
Rigid Stamp

This study proposes analytical and computational methods for the solution of the sliding frictional contact problem of an anisotropic laterally graded layer loaded by an arbitrarily shaped rigid stamp. The plane-strain orthotropy prevails in the layer which is bonded to a rigid foundation. Each of four orthotropic stiffness coefficients is exponentially varied through the lateral direction of the elastic layer. The Fourier transformations of the field variables are employed in the formulation. The gradient of a displacement component on the surface is then converted to a singular integral equation of the second kind. The singular integral equation is solved by means of the Gauss–Jacobi quadrature integration techniques, a collocation method, and a recursive integration method for the Cauchy integral considering the flat and triangular stamp profiles. The finite element method solutions of the same contact problems are performed using the augmented Lagrange method which is implemented in virtue of ANSYS design parametric language. An iterative algorithm is additionally utilized for the (incomplete) triangular stamp problem to conveniently reach the solutions for predetermined contact lengths. The convergence and comparative analyses are carried out to elucidate the trustworthiness of the analytical and computational methods proposed. Moreover, the parametric analyses infer that the contact-induced damage risks can be effectively alleviated upon tuning the degree of orthotropy and the lateral heterogeneity of the elastic layer.

A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

2017 ◽  
Vol 24 (2) ◽  
pp. 448-464 ◽  
Author(s):  
Jie Yan ◽  
Changwen Mi ◽  
Zhixin Liu
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Singular Integral Equation ◽  
Contact Problem ◽  
Singular Integral ◽  
Material Properties ◽  
Elastic Layer ◽  
Coated Substrate ◽  
Receding Contact ◽  
Contact Size

In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are allowed to vary exponentially along its thickness. A distributed traction load applied over a finite segment of the layer surface presses the layer and the coated substrate against each other. It is further assumed that the receding contact between the layer and the coated substrate is frictionless. In the absence of body forces, Fourier integral transforms are used to convert the governing equations and boundary conditions of the plane receding contact problem into a singular integral equation with the contact pressure and contact size as unknowns. Gauss–Chebyshev quadrature is subsequently employed to discretize both the singular integral equation and the force equilibrium condition at the contact interface. An iterative algorithm based on the method of steepest descent has been proposed to numerically solve the system of algebraic equations, which is linear for the contact pressure but nonlinear for the contact size. Extensive case studies are performed with respect to the coating inhomogeneity parameter, geometric parameters, material properties, and the extent of the indentation load. As a result of the indentation, the elastic layer remains in contact with the coated substrate over only a finite interval. Exterior to this region, the layer and the coated substrate lose contact. Nonetheless, the receding contact size is always larger than that of the indentation traction. To validate the theoretical solution, we have also developed a finite-element model to solve the same receding contact problem. Numerical results of finite-element modeling and theoretical development are compared in detail for a number of parametric studies and are found to agree very well with each other.

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